ANGLE BISECTORS

(Chapter 2.2)

VOCABULARY

• Angle Bisector: a ray that divides an angle into two congruent angles

110

A

B C

D

BD bisects ABC, and m ABC = 110.

Therefore, the m ABD and m BDC is half of m ABC.110

2 = 55m ABD and m BDC

is 55.

EXAMPLE #1

m GHJ = 52 HK is the angle bisector.

m GHK = m JHK =&26 26

EXAMPLE #2

m GHJ = 90 HK is the angle bisector.

m GHK = m JHK =&45 45

EXAMPLE #3

m GHJ = 161 HK is the angle bisector.

m GHK = m JHK =&80.5 80.5

Finding Angle Measures and

Classifying Angles

m

m

m

LMP

NMP

LMN

MP bisects LMN

46

46

92

obtuse

m

m

m

RQS

PQS

PQR

QS bisects PQR

29

29

58

acute

m

m

m

RQS

PQS

PQR

QS bisects PQR

45

45

90

right

m

m

m

RQS

PQS

PQR

QS bisects PQR

60

60

120

obtuse

RQ bisects PRS. Find the value of x.6x + 1 = 85

-1 -16x = 84

6x = 846 6x = 14

9x = 8x + 3-8x -8x

x = 3

x + 12 = 55-12 -12

x = 43